An iterative solution of one-dimensional rough surface scattering problems based on a factorization of the Helmholtz operator

An iterative series solution for two-dimensional scattering problems derived from a minimally coupled factorization of the Helmholtz equation is presented. The Helmholtz operator is represented as a product of one-way wave operators and a corresponding coupling operator. Coupling between oppositely propagating fields is shown to be predominantly localized and this permits an accurate and numerically efficient approximation of the coupling operator. The resulting iterative series is shown to be rapidly convergent for the problem of scattering from impenetrable rough surfaces.